This project walks students through computing the perimeter and area of the Koch Snowflake as an application of geometric series. Students then create their own fractal and perform similar computations.

This project introduces the idea of recursive sequences. Students then prove that a given recursive sequence converges and find its limit. The final portion of the project is a derivation and investigation of the Fibonacci Sequence and the Golden Ratio.

For an electron moving in a circular path in a magnetic field, if we know the magnetic field strength, accelerating voltage, and radius of the electron's trajectory, then we can make an estimation of the electron's charge to mass ratio. We calculated an average charge to mass ratio of \(2.08 \times 10^{11} \pm 1.81 \times 10^8\) Coulombs per kilogram.

In this project, students create a two-dimensional shape with nonuniform density, finds its center of mass, and hang it from a mobile. The various portion of the project address the differences and relationships between computing the center of mass of a discrete set of point masses and a lamina.
Included here is also a sample solution to help students formulate their own well-written solutions. Also, in the LaTeX code are a few comments to address some of the basics of LaTeX and Overleaf.